I started recently defending wide range vs bu 2bb open from BB, but I think I dont know how to play with hands like this which rarely hits the board. Should I fold this kind of board, and play only on small boards where I hit something, fold otherwise. I think the problem is that I try to win each pot.
Here I raise because I have backdoor fd, and I thought I can represent straight, or two pairs, also it is tought for him to call down marginal hands.

He folds 55% to raise after cbet, and opens 50% bu.

when I raise cbet like here with backdoor fd, then I should continue barreling only if I hit fd on turn? Then barrel river on blank?

Just give up on this board.. You cannot represent much either because you 3bet a lot of the higher cards and pairs agaist BU minopen. I think playing back on lower boards will be fine, even if you just hit like a gutshot but definitely better than attacking this board.